Microstructure of two-phase random media. V. The n-point matrix probability functions for impenetrable spheres

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Abstract
We examine the two‐ and three‐point matrix probability functions for a two‐phase random and homogeneous system of impenetrable spheres. For such a system, we give an exact analytical expression for the two‐point matrix function S2 through second order in the number density of particles. Moreover, the two‐point matrix function is evaluated, for the first time, for a very wide range of densities. We also discuss the evaluation of the three‐point matrix function S3 for an impenetrable‐sphere system and provide new expressions that may be used to estimate it.